1. The problem statement, all variables and given/known data Hello again. First of all thanks to anyone who has replied to my previous questions. Now, the question that troubles me is: We are given a matrix A2x2 with some random values and we are asked to say if there is a linear map which has A as its map for the standar basis. A= 2 1 -5 8 2. Relevant equations 3. The attempt at a solution If A is the matrix of some linear map for the standar basis that means that: f(1,0)=2(1,0) -5(0,1) f(0,1)=1(1,0) +8(0,1) so f(1,0)=(2,-5) and f(0,1)=(1,8) Although the question only asks to say if such a linear map exists (it obviously does but i dont know how to prove it) I would be glad if someone could instruct me on finding formulas for linear maps when we have their matrix.